Base field 6.6.434581.1
Generator \(w\), with minimal polynomial \(x^{6} - 2x^{5} - 4x^{4} + 5x^{3} + 4x^{2} - 2x - 1\); narrow class number \(1\) and class number \(1\).
Form
Weight: | $[2, 2, 2, 2, 2, 2]$ |
Level: | $[71, 71, 2w^{5} - 6w^{4} - 4w^{3} + 17w^{2} - w - 6]$ |
Dimension: | $1$ |
CM: | no |
Base change: | no |
Newspace dimension: | $9$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q$.
Norm | Prime | Eigenvalue |
---|---|---|
13 | $[13, 13, -w^{5} + 3w^{4} + 2w^{3} - 9w^{2} + w + 4]$ | $\phantom{-}4$ |
13 | $[13, 13, -w^{2} + w + 2]$ | $-2$ |
27 | $[27, 3, 2w^{5} - 4w^{4} - 7w^{3} + 9w^{2} + 4w - 2]$ | $-4$ |
27 | $[27, 3, -2w^{5} + 5w^{4} + 5w^{3} - 12w^{2} - w + 5]$ | $-4$ |
29 | $[29, 29, w^{3} - 2w^{2} - 2w + 3]$ | $\phantom{-}6$ |
29 | $[29, 29, 2w^{5} - 4w^{4} - 7w^{3} + 8w^{2} + 4w - 2]$ | $\phantom{-}0$ |
43 | $[43, 43, -w^{5} + 3w^{4} + w^{3} - 6w^{2} + 3w + 1]$ | $-8$ |
43 | $[43, 43, -w^{4} + w^{3} + 5w^{2} - 4]$ | $\phantom{-}4$ |
49 | $[49, 7, w^{5} - 4w^{4} + 11w^{2} - 3w - 4]$ | $\phantom{-}8$ |
64 | $[64, 2, -2]$ | $\phantom{-}7$ |
71 | $[71, 71, 2w^{5} - 6w^{4} - 4w^{3} + 17w^{2} - w - 6]$ | $-1$ |
71 | $[71, 71, 2w^{4} - 4w^{3} - 6w^{2} + 7w + 2]$ | $\phantom{-}12$ |
71 | $[71, 71, -w^{5} + 3w^{4} + 2w^{3} - 7w^{2} - w]$ | $\phantom{-}12$ |
71 | $[71, 71, -2w^{5} + 5w^{4} + 6w^{3} - 14w^{2} - 3w + 5]$ | $\phantom{-}0$ |
83 | $[83, 83, -3w^{5} + 7w^{4} + 9w^{3} - 17w^{2} - 5w + 5]$ | $-6$ |
83 | $[83, 83, 3w^{5} - 6w^{4} - 10w^{3} + 12w^{2} + 5w - 2]$ | $-6$ |
83 | $[83, 83, -2w^{5} + 5w^{4} + 5w^{3} - 11w^{2} - 3w + 3]$ | $\phantom{-}12$ |
83 | $[83, 83, 3w^{5} - 7w^{4} - 8w^{3} + 15w^{2} + 2w - 4]$ | $-12$ |
97 | $[97, 97, -3w^{5} + 6w^{4} + 10w^{3} - 12w^{2} - 5w + 3]$ | $-8$ |
97 | $[97, 97, w^{5} - 2w^{4} - 4w^{3} + 5w^{2} + 5w - 3]$ | $-10$ |
Atkin-Lehner eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
$71$ | $[71, 71, 2w^{5} - 6w^{4} - 4w^{3} + 17w^{2} - w - 6]$ | $1$ |